Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
\[x \cdot e^{y \cdot y}\]
↓
\[\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]
x \cdot e^{y \cdot y}
↓
\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}
double f(double x, double y) {
        double r414703 = x;
        double r414704 = y;
        double r414705 = r414704 * r414704;
        double r414706 = exp(r414705);
        double r414707 = r414703 * r414706;
        return r414707;
}
↓
double f(double x, double y) {
        double r414708 = x;
        double r414709 = y;
        double r414710 = r414709 * r414709;
        double r414711 = exp(r414710);
        double r414712 = sqrt(r414711);
        double r414713 = r414708 * r414712;
        double r414714 = exp(r414709);
        double r414715 = 2.0;
        double r414716 = r414709 / r414715;
        double r414717 = pow(r414714, r414716);
        double r414718 = r414713 * r414717;
        return r414718;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto x \cdot \color{blue}{\left(\sqrt{e^{y \cdot y}} \cdot \sqrt{e^{y \cdot y}}\right)}\]

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{y \cdot y}}}\]
  5. Using strategy rm

  6. Applied add-log-exp0.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{e^{\color{blue}{\log \left(e^{y}\right)} \cdot y}}\]

  7. Applied exp-to-pow0.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \sqrt{\color{blue}{{\left(e^{y}\right)}^{y}}}\]

  8. Applied sqrt-pow10.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot \color{blue}{{\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}}\]

  9. Final simplification0.0

    \[\leadsto \left(x \cdot \sqrt{e^{y \cdot y}}\right) \cdot {\left(e^{y}\right)}^{\left(\frac{y}{2}\right)}\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))